1. Field of the Invention
This invention relates to a method of determination of fuselage shape, and a fuselage front section shape, to suppress sonic boom without increasing the wave drag of supersonic aircraft.
2. Description of the Related Art
In general, in order to satisfy conditions for economy and environmental compatibility, a supersonic aircraft must [be designed] so as to suppress wave drag caused by shock waves and sonic boom, which is an acoustic phenomenon affecting persons, animals, buildings and other structures on the ground.
The axisymmetric shape in which the area cross-sectional distribution with respect to the length position is longitudinally symmetric (a Sears-Haack body; see Sears, W. R., “On Projectiles of Minimum Wave Drag”, Quart. Appl. Math., Vol. 14, 1947), shown in FIG. 12, is known as the shape of a body in supersonic flight with minimum wave drag. In order to reduce wave drag of an supersonic aircraft, the equivalent body of revolution of an airplane which has the area distribution of the circumferential average of the area, projected in the axial direction of the aircraft, of the cross-sectional area cut by the Mach plane (the plane whose normal vector is inclined by an angle μ=sin−1(1/M) with respect to the axial direction), determined by the Mach number at which the aircraft flies, deemed to be equivalent to this Sears-Haack body. The method used to design such aircraft is called the Area Rule design method.
Research has been conducted over many years on methods to reduce sonic boom; the most effective method involves changing the pattern of the shock wave generated through innovations in the aircraft body shape, in order to reduce the sonic boom intensity on the ground. Shock waves generated from the various components of an ordinary supersonic aircraft exhibit a phenomenon in which, in the process of propagation in air, waves entailing larger changes in pressure propagate more rapidly in air, and as a consequence the shock waves are units as two strong shock waves emanating from the nose and from the tail sections, and are observed on the ground as an N pressure wave accompanied by two large increases in pressure. The shock wave created and caused to propagate by the supersonic aircraft propagates in the form of a cone until reaching the ground, as shown in FIG. 13-2. At this time, the N pressure wave comprises a shock wave which changes suddenly from atmospheric pressure to high pressure, due to the nose portion, and a shock wave which, after declining somewhat is returned suddenly from low pressure to high pressure due to the tail portion, as shown in FIG. 13-1. The sonic boom of the Concorde, which is representative of supersonic aircraft, is from 2 to 3 psf, which is said to be equivalent to the sound of lightning striking close by.
Because supersonic flight is limited in airspace over terrain where noise due to sonic boom is a problem, commercialization of supersonic passenger aircraft has been difficult. The above-described method of reducing sonic boom involves forming a low-sonic-boom-pressure waveform, which is not an ordinary N wave, by modifying the aircraft shape and suppressing the unification of shock waves. George and Seebass have proposed boom minimization, including the trailing-edge wave, based on near-field theory, and studying two types of pressure waves, the “minimum over-pressure waveform” shown in the upper of FIG. 13-3, and the “minimum-shock waveform” shown in the lower of FIG. 13-3; and in Seebass, A. R. and George, A. R., “Design and Operation of Aircraft to Minimize Their Sonic Boom”, Journal of Aircraft, Vol. 11 No. 9, pp. 509-517, 1974, they present a theoretical study which focuses on the sum of equivalent cross-sectional area distributions determined from the cross-sectional area distribution of an aircraft forming a low-sonic-boom-pressure waveform and the lift distribution. This focuses on the shape of the fuselage as one factor due to which the aircraft body causes pressure changes in the atmosphere, and on the second factor of the reaction to the lift received by the wings; a theoretical analysis is thus presented in which, while the reaction to the lift has a downward directionality, an equivalent cross-sectional area is posited which takes the [reaction to the lift] to be in all directions, similarly to the aircraft body, so that when the sum of the equivalent cross-sectional area distribution determined from the cross-sectional area of the aircraft and the lift distribution has a prescribed distribution, low sonic boom can be realized. However, if a shape having such an equivalent cross-sectional area distribution is computed, the nose shape is blunt, resulting in considerable airframe drag. Subsequently, in Darden, C. M., “Sonic-Boom Minimization with Nose-Bluntness Relaxation”, NASA TP-1348, 1979, Darden proposed a method and program which use the cross-sectional area distribution of George and Seebass to reduce the airframe drag arising from this nose portion.
Because a shock wave has the property that waves with greater increases in pressure propagate through the air more rapidly, in order to suppress the unification of shock waves, it is effective to make the nose shape blunt to cause an intense shock wave, and to weaken the rearward shock wave. However, such a blunt nose shape cannot satisfy the [conditions of the] above-described Area Rule design to minimize wave drag, and an increase in wave drag is unavoidable. The equivalent cross-sectional area distribution of an aircraft forming a low-sonic-boom pressure waveform, described in the above work by George and Seebass, also indicates that the nose shape will be blunt; and the design method of Darden to relax the degree of bluntness of the nose shape can reduce the wave drag with only a small increase in the sonic boom intensity, but as indicated in FIG. 14 there is a trade-off between sonic boom and wave drag, and modifying the airframe shape has the effect of worsening one or the other, or possibly both. Thus there has not yet been found an ideal aircraft shape which achieves [the aims of] both the Area Rule design, and low sonic boom design.
In light of such circumstances, the inventors' research group has conducted research with the aim of developing a method of determining the fuselage shape of a supersonic aircraft which reduces sonic boom without increasing wave drag. Because sonic boom is a shock wave which propagates downward from the airframe, the upper-surface shape of the airframe is assumed not to affect the sonic boom intensity, and so an attempt was made to suppress the increase in wave drag by replacing the fuselage upper-surface shape of a low-sonic-boom airframe with a low-wave-drag shape. An airframe model of a low-wave-drag fuselage of the prior art is shown on the right in FIG. 15, an airframe model of a conventional low-sonic-boom fuselage is shown on the upper left, and an airframe model of a low-wave-drag/low-boom fuselage proposed by the research group of the inventors is shown on the lower-left. That is, as is clear from the drawings seen from the forward direction of the airframe, the fuselage of a conventional low-wave-drag airframe model is narrow, the fuselage of a conventional low-sonic-boom airframe model is wide, and the fuselage of the low-wave-drag/low-boom airframe model proposed by the inventors' research group combines completely different shapes as the upper and lower surface shapes of the fuselage. In other words, as the upper half the airframe model of a conventional low-wave-drag fuselage is adopted, and as the lower half of the fuselage the airframe model of a conventional low-sonic-boom fuselage is adopted, in an airframe shape which combines the two.
The inventors' research group has fabricated mock-ups of a conventional low-drag fuselage airframe model, a conventional low-sonic-boom fuselage airframe model, and of the low-drag/low-sonic-boom fuselage airframe model proposed by the inventors' research group. [These were] used in wind tunnel experiments to obtain various design data, results of which were reported in Makino, Y. et al, “Nonaxisymmetrical Fuselage Shape Modification for Drag Reduction of Low-Sonic-Boom Airplane”, AIAA Journal, Vol. 41 No. 8, pp. 1413-1420, 2003. The graphs shown in FIG. 16 compare the cross-sectional area distributions of the three airframes; circles (◯) denote airframe cross-sectional area, squares (□) denote the equivalent cross-sectional area of lift, and triangles (Δ) are the sum of the former two; broken lines indicate the theoretical optimum distribution. As is clear from these drawings, because the upper-surface shape is replaced with a low-drag shape in the airframe model having a low-drag/low-boom fuselage, the cross-sectional area distribution deviates considerably from the conventional theoretical target value for low sonic boom.
However, upon viewing the results of pressure waveform measurements obtained from wind tunnel experiments using mock-ups of these airframe models, the waveforms shown in FIG. 17 were obtained. Because these are values measured in wind tunnel experiments, they are not far-field pressure measurements, but are equivalent to pressure measurements in the near field. On comparing the three airframes, the conventional low-drag fuselage is the graph plotted with circles (◯); the pressure change due to the airframe tip portion is comparatively small, but there is a large pressure fluctuation in the center portion of the airframe. There is no great difference in the results for the airframe model with the conventional low-sonic-boom fuselage, denoted by triangles (Δ), and the airframe model with the low-drag/low-boom fuselage proposed by the inventors' research group, denoted by diamond shapes (⋄); although the pressure change due to the airframe tip portion is comparatively large, and there is a large pressure change in the center portion of the airframe as well, the magnitude is much smaller than for the conventional low-drag fuselage. The large pressure change due to the airframe center portion of the conventional low-drag fuselage becomes a wave and, in the course of propagating through the atmosphere, is unified with the wave of comparatively small pressure fluctuation of the front, to impart a substantial pressure fluctuation on the ground. On the other hand, in the pressure waveforms resulting from the airframe model of the conventional low-sonic-boom fuselage and the airframe model of the low-drag/low-boom fuselage proposed by the inventors' research group, the comparatively large pressure change due to the airframe tip portion propagates fairly rapidly through the atmosphere, and the subsequent large pressure fluctuation due to the airframe center portion does not overlap with the former, so that the sonic boom intensity does not become large. Thus the airframe model with low-drag/low-boom fuselage proposed by the inventors' research group achieves low sonic boom. Also, upon measuring the force on the airframe in the axial direction, the resulting data in the graph shown in FIG. 18 were obtained. The vertical axis plots the drag CD, and the horizontal axis is the dimensionless coefficient of lift CL. Filled circles (●) denote data for the conventional low-boom airframe model; empty circles (◯) are data for the conventional low-drag airframe model; and diamond shapes (⋄) denote data for the airframe model with low-drag/low-boom fuselage proposed by the inventors' research group. As is clear from this graph, substantially the same reduced drag as in the conventional low-drag airframe model is attained.
Based on the above experimental results, and given the supposition that the upper surface shape of the airframe does not affect the sonic boom intensity below the airframe, it was verified that an airframe model in which the upper surface shape of an airframe designed to reduce wave drag is replaced with an Area Rule fuselage, will exhibit substantially low drag, and moreover can achieve low sonic boom.